Letters in Biomathematics Volume I, issue 2 (2014) An International Journal http://www.lettersinbiomath.org
Research Article
Vertical Transmission in a Two-Strain Model of Dengue Fever
David Murillo1, Susan A. Holechek1,2,*, Anarina L. Murillo1, Fabio Sanchez1,3, Carlos Castillo-Chavez1
Abstract The role of vertical transmission in vectors has rarely been addressed in the study of dengue dynamics and control, in part because it was not considered a critical population-level factor. In this paper, we apply the pioneering model- ing ideas of Ross and MacDonald, motivated by the context of the 2000–2001 dengue outbreak in Peru, to assess the dynamics of multi-strain competition. An invading strain of dengue virus (DENV-2) from Asia rapidly circulated into Peru eventually displacing DENV-2 American. A host-dengue model that con- siders the competing dynamics of these two DENV-2 genotypes, the resident or the American type and the invasive more virulent Asian strain, is introduced and analyzed. The model incorporates vertical transmission by DENV-2 Asian a potentially advantageous trait. Conditions for competitive exclusion of dengue strains are established. The model is used to show that lower transmission rates of DENV-2 Asian are sufficient for displacing DENV-2 American in the presence of vertical transmission. Keywords: vector-host model, dengue, epidemiology, vertical transmission, Peru
1 Introduction
Sir Ronald Ross (1911) first introduced mathematical models in the study of vector-borne disease dynamics, in the context of Malaria [11, 66]. Over a decade later Kermark and McK- endrick [41] adapted his work in the context of communicable diseases. Today a simplified version of the Kermark McKendrick model is found in most elementary calculus textbooks and is known as the Susceptible-Infected-Recovered or SIR model (Figure 1). The SIR